Top-scorer Michu gave the Swans the perfect start at Carrow Road but goals from Robert Snodgrass and Michael Turner looked to have won it for the hosts.
But Luke Moore salvaged a point for the visitors with 15 minutes remaining as Michael Laudrup's Capital One Cup-winning side halted a run of three league defeats on the spin.
Williams said: "People have obviously been looking at our results and saying we have stopped playing.
"But we are still working hard and I honestly don't see it that way. We don't see our season as over, far from it.
"My impression is that the team has just been having a bit of a wobble recently, nothing more.
"I'm not really fussed about what people have been saying but after three losses we needed to stop the rot and we've done that.
"On a different day we could easily have won and I think we showed great character to come back from 2-1.
"Now we just have to make sure that we finish the season strongly."
While Michu missed two late chances to win the game, Williams kept the Spaniard's contribution to the cause in perspective.
"We are never going to complain about him missing a few chances after all the goals he's scored for us this season," he said.
"He scored one goal and he was just unlucky not to put one of the other chances away."